A THREE-DIMENSIONAL MIXED FINITE ELEMENT SCHEME FOR NONLINEAR QUASI-STATIC EDDY CURRENT PROBLEM

Resumo

We present the first fully discrete mixed finite element formulation
for the stationary three-dimensional p-curl problem. The method relies on
N´ed´elec edge elements and Raviart–Thomas face elements, and yields a discrete
scheme that is consistent with the underlying continuous mixed formulation.
The core of the analysis is the proof of existence and uniqueness of the discrete
solution for p > 2. This work provides the first rigorous numerical framework
for the mixed finite element approximation of the three-dimensional p-curl
problem, and paves the way for future extensions, including non-homogeneous
boundary conditions, the fully time-dependent problem, and the implementation
of the method on representative test cases.